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arXiv · 1601.07816

A note on twisted Dirac operators on closed surfaces

Volker Branding
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Abstract

We derive an inequality that relates nodal set and eigenvalues of a class of twisted Dirac operators on closed surfaces and point out how this inequality naturally arises as an eigenvalue estimate for the $\rm Spin^c$ Dirac operator. This allows us to obtain eigenvalue estimates for the twisted Dirac operator appearing in the context of Dirac-harmonic maps and their extensions, from which we also obtain several Liouville type results.

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Volker Branding. 2018-06-04. A note on twisted Dirac operators on closed surfaces. https://doi.org/10.1016/j.difgeo.2018.05.006

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